Linear mapping/Bijective/Inverse mapping linear/Fact

Let ${}K$ be a field, and let ${}V$ and ${}W$ be ${}K$-vector spaces. Let

$\varphi \colon V\longrightarrow W$

be a bijective linear map.

Then also the

inverse mapping

$\varphi ^{-1}\colon W\longrightarrow V$

is linear.

Write a proof